Secret Messages Throughout History

Number Theory · Axiom Academy

INTRO Secret Messages Throughout History From ancient Rome to modern encryption, discover the mathematical magic of cryptography. In 58 BC, Julius Caesar needed to send secret military commands. His solution? Shift every letter by 3 positions in the alphabet. Try it yourself! Now you're the cryptographer! Type a secret message and watch it get encoded with your chosen shift. Here's an intercepted message: "JHLZHY JPWOLY PZ LHZF" . Can you crack it? Substitution Ciphers: More Complex What if instead of shifting, we randomly scramble the entire alphabet? This creates 26! (403,291,461,126,605,635,584,000,000) possible keys! Today's encryption doesn't just shift letters - it uses prime numbers, modular arithmetic, and one-way functions. Prime Numbers: RSA uses products of huge primes Modular Arithmetic: All operations work in finite fields One-Way Functions: Easy to compute, hard to reverse Discrete Logarithms: The basis of Diffie-Hellman key exchange

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